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2008, Volume 5, Issue 2: 337-354. Doi: 10.3934/mbe.2008.5.337
This issue Previous Article Principal eigenvalue for an elliptic problem with indefinite weight on cylindrical domains Next Article Simulation of single-species bacterial-biofilm growth using the Glazier-Graner-Hogeweg model and the CompuCell3D modeling environment

An observer for a nonlinear age-structured model of a harvested fish population

  • 1.

    Laboratoire d’Analyse Numérique et d’Informatique (LANI), UFR de Sciences Appliquées et de Technologie., Université Gaston Berger. B.P. 234 Saint-Louis,

  • 2.

    INRIA-Lorraine and University Paul Verlaine-Metz, LMAM-CNRS UMR 7122, ISGMP Bat. A, Ile du Saulcy, 57045 Metz Cedex 01

  • 3.

    Laboratoire d’Analyse Mathématique des Equations (LAME), Faculté des Sciences et Techniques. Université de Ouagadougou, B.P. 7021 Ouagadougou,

  • 4.

    ISTA/ZI, B.P 399, Settat, Maroc

Received:  May 31, 2007
Revised:  December 31, 2007
Published:  February 2008
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    Abstract
  • We consider an age-structured model of a harvested population. This model is a discrete-time system that includes a nonlinear stock-recruitment relationship. Our purpose is to estimate the stock state. To achieve this goal, we built an observer, which is an auxiliary system that uses the total number of fish caught over each season and gives a dynamical estimation of the number of fish by age class. We analyse the convergence of the observer and we show that the error estimation tends to zero with exponential speed if a condition on the fishing effort is satisfied. Moreover the constructed observer (dynamical estimator) does not depend on the poorly understood stock-recruitment relationship. This study shows how some tools from nonlinear control theory can help to deal with the state estimation problem in the field of renewable resource management.
    Mathematics Subject Classification: Primary: 34D23, 92D25,93B07, 93C10, 93C41; Secondary: 93B50.

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